Basics of measurement resolution

In electronic instrumentation, resolution is a measure of the distance in amplitude at which we can distinguish between two points on a waveform. This is not the same as accuracy, which is a measure of how closely a waveform as displayed or measured agrees with the signal at the instrument’s input.

One of the principal endeavors of those who work in this field is to identify, measure and display weak and transitory events in the presence of high-amplitude and/or high-frequency signals or in the presence of electrical noise. There are a number of strategies for dealing with these two common problems, and we shall look at some of them.

They are relevant in variable frequency drives (VFDs), which exist in great numbers world-wide. They allow ac motors to power everything from elevators, where smooth transitions are needed, to high-speed centrifuges in clandestine nuclear-enrichment laboratories.

A VFD along with the accompanying motor controller typically sits in a floor-to-ceiling steel enclosure. When the motor overheats or trips out, the first thing to do is to perform a power-quality study. There are elaborate, expensive instruments that perform the required measurements, but realistically the hand-held, battery-powered oscilloscope in the field or bench-type instrumentation in the lab, such as a spectrum analyzer, is first on the scene.

A differential probe as it might be used to check two of the outputs from a VFD.

In many applications, we are looking at 480 Vac with potentials both inside and outside the VFD referenced to but floating above premises ground. To avoid fault current, a differential probe or hand-held oscilloscope with inputs isolated from ground and from one another is the sensible answer. Then, we can begin by looking at the individual phase waveforms. A VFD requires high-quality, closely-balanced phases. It is often necessary to take continuous readings over an extended period of time, as appropriate to the electrical environment.

The next place to look is inside the enclosure, at the dc bus. Here again, we need to measure a small signal such as ac ripple riding on the high dc voltage. If the VFD operates on 480 Vac at its input, the voltage on the dc bus will actually be higher, 678 Vdc! This is because it relates not to the ac RMS system voltage at the VFD input, but rather to the internal full-wave rectifier output, which is derived from the ac peak-to-peak voltage.

In an oscilloscope display, any ac ripple will be decisively scaled down because of the large dc component. The remedy in a Tektronix MDO3000 oscilloscope is to press the relevant channel button, which opens the horizontal channel signal menu. The first menu selection is Coupling, and the associated soft key permits the user to choose between dc, which is the default, and ac.

DC Coupling is used most of the time. It should be called ac-dc Coupling so that the impression is not conveyed that the AC component is suppressed. Actually, dc Coupling does nothing, permitting the signal to pass through unmodified. AC Coupling, in contrast, places a capacitance in series with the signal, eliminating the dc component. Thus, the ac ripple (viewed in ac coupling) in a VFD dc bus is not scaled down within the oscilloscope by the presence of the high dc voltage, and it can be accurately measured and displayed.

Besides scaling, the other big issue that impacts signal resolution in an oscilloscope is noise. This is random, wide-band electrical energy that can be inherent in the source of a signal of interest, generated within the instrument that is intended to process and display that signal or picked up by cabling or other media that convey the signal from source to receiver. Each of these types of noise has qualities which may help us to identify it and obtain clues regarding mitigation strategies.

Any conductive body including a resistor just sitting on a shelf in a warehouse and not connected to anything, always exhibits across it a small but real voltage. If the leads are shunted together a small current (countless trillions of electrons per unit of time) will continuously cross the junction. This current, of course, is ac and the waveform if you could amplify and display it would have a random fluctuating appearance and the frequency span would be enormous.

In any electronic equipment, all internal conductive devices including semiconductors and wiring contribute to this noise voltage. This voltage constitutes the noise floor that we see in the display of an oscilloscope. Noise is inevitable. When a signal is displayed in an oscilloscope or spectrum analyzer, depending on the instrument’s settings, the user sees a noise floor. While the noise floor can be lowered but in principle never eliminated, it will also become more prominent as the instrument’s sensitivity is improved.

In a time domain display, noise is seen as a noticeable thickening of the trace until triggering is lost and the waveform becomes an indistinct blur of light. In the frequency domain, viewed in a spectrum analyzer or oscilloscope set to Math>FFT, the noise floor appears as a rapidly and randomly fluctuating roughly horizontal line below the spectral display of the signal of interest. It is located below the signal because relative to the Y-axis it has less power in decibels. If the signal amplitude declines below the noise amplitude, the signal falls below the noise floor and is lost from the point of view of the user.

This harmful effect can easily be mitigated using either of two tools that are built into modern digital oscilloscopes and may be summoned by pressing a couple soft keys. These tools are Bandwidth Limiting and Signal Averaging (sometimes called Waveform Averaging).

To see how Bandwidth Limiting works in the Tektronix MDO3000 oscilloscope, press AFG and dial-up Sine Wave. Press Output Settings and add 30% noise. Notice that the trace is grossly thickened and triggering is lost. Bandwidth Limiting is accessed by pressing the relevant channel button. The horizontal channel signal menu appears across the bottom of the display and the fourth menu selection is Bandwidth. Pressing the associated soft key, the vertical Bandwidth menu comes up on the right. Full bandwidth, of course, is the default.

When the bandwidth is limited to 250 MHz, the signal is only slightly improved. This is in part dependent upon the sine wave frequency, which may be adjusted in AFG>Settings. Cutting bandwidth to 20 MHz greatly improves the waveform, a relatively small amount of noise remaining as shown by the thickened trace. Bandwidth Limiting is a quick and easy way to cut through a lot of noise, but as we have seen it is not entirely effective. Moreover, it will not work when significant bandwidth is required to display a high-frequency signal.

Waveform Averaging eliminates those disadvantages, but for it to work the waveform under investigation must be periodic and repetitive. To illustrate, with the same 30% noise added, display the sine wave. (Waveform averaging can be difficult to find if you don’t know where to look.) Be sure to turn Bandwidth back to Full. Press Acquire and in the horizontal menu at the bottom, press the soft key associated with Mode. In the vertical menu at the right, press the soft key associated with Average.

Waveform Averaging uses successive acquisitions to obtain an average, and because the periodic waveform remains the same while noise, a random phenomenon, varies in each acquisition, Waveform Averaging successfully eliminates noise from the display, more so as the number of acquisitions is increased. By means of Multipurpose Knob a, this number can be set by the user, varying from two to 512. At 512, the trace is quite thin but the amplitude pulsates. Going back to AFG and eliminating the additive noise, the pulsating ceases and the trace is thin, even more so than when Waveform Averaging is turned off and the sine wave from AFG is observed. That slight amount of observed noise probably derives from the internal noise floor.